US President Donald Trump has broken the ice with Chinese President Xi Jinping in a letter that said he looked forward to working with him to develop relations, although the pair haven't spoken directly since Trump took office.

The letter thanked Xi for his congratulatory note on Trump's inauguration and wished the Chinese people a prosperous Lunar New Year of the Rooster, the White House said in a statement on Wednesday.

"President Trump stated that he looks forward to working with President Xi to develop a constructive relationship that benefits both the United States and China," it said.

China said on Thursday it attached great importance to China-US ties after confirming it received the letter.

At a daily press briefing in Beijing, Chinese Foreign Ministry spokesman Lu Kang said China commended Trump for sending Lunar New Year greetings to the Chinese people and said co-operation between the two countries was the only option.

Trump and Xi have yet to speak directly since Trump took office on January 20, although they did talk soon after Trump won the US presidential election in November.

Diplomatic sources in Beijing say China has been nervous about Xi being left humiliated in the event a call with Trump goes wrong and the details are leaked to the US media.